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    <ol class="post-toc"><li class="post-toc-item post-toc-level-3"><a class="post-toc-link" href="#位运算之运算符"><span class="post-toc-number">1.</span> <span class="post-toc-text">位运算之运算符</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#与运算符"><span class="post-toc-number">1.0.1.</span> <span class="post-toc-text">与运算符</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#或运算符"><span class="post-toc-number">1.0.2.</span> <span class="post-toc-text">或运算符</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#异或运算符"><span class="post-toc-number">1.0.3.</span> <span class="post-toc-text">异或运算符</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#非运算符"><span class="post-toc-number">1.0.4.</span> <span class="post-toc-text">非运算符</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#左移和右移运算符"><span class="post-toc-number">1.0.5.</span> <span class="post-toc-text">左移和右移运算符</span></a></li></ol></li></ol></li><li class="post-toc-item post-toc-level-3"><a class="post-toc-link" href="#加法运算"><span class="post-toc-number">2.</span> <span class="post-toc-text">加法运算</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#加法运算的原理"><span class="post-toc-number">2.0.1.</span> <span class="post-toc-text">加法运算的原理</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#代码示例"><span class="post-toc-number">2.0.2.</span> <span class="post-toc-text">代码示例</span></a></li></ol></li></ol></li><li class="post-toc-item post-toc-level-3"><a class="post-toc-link" href="#减法运算"><span class="post-toc-number">3.</span> <span class="post-toc-text">减法运算</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#减法运算的原理"><span class="post-toc-number">3.0.1.</span> <span class="post-toc-text">减法运算的原理</span></a></li><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#代码示例-1"><span class="post-toc-number">3.0.2.</span> <span class="post-toc-text">代码示例</span></a></li></ol></li></ol></li><li class="post-toc-item post-toc-level-3"><a class="post-toc-link" href="#乘法运算"><span class="post-toc-number">4.</span> <span class="post-toc-text">乘法运算</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#乘法运算的原理"><span class="post-toc-number">4.0.1.</span> <span class="post-toc-text">乘法运算的原理</span></a></li></ol></li></ol></li><li class="post-toc-item post-toc-level-3"><a class="post-toc-link" href="#除法运算"><span class="post-toc-number">5.</span> <span class="post-toc-text">除法运算</span></a><ol class="post-toc-child"><li class="post-toc-item post-toc-level-5"><a class="post-toc-link" href="#原理"><span class="post-toc-number">5.0.1.</span> <span class="post-toc-text">原理</span></a></li></ol></li></ol></li></ol>
    <div class="content-article">
        <h3 id="位运算之运算符"><a href="#位运算之运算符" class="headerlink" title="位运算之运算符"></a>位运算之运算符</h3><ul>
<li><p>&amp; 与</p>
</li>
<li><p>| 或</p>
</li>
<li><p>^ 异或</p>
</li>
<li><p>~ 非</p>
</li>
<li><p>&lt;&lt; 左移</p>
</li>
<li><p>>> 右移</p>
</li>
</ul>
<h5 id="与运算符"><a href="#与运算符" class="headerlink" title="与运算符"></a>与运算符</h5><p>假设对两个·二进制数做与运算如下:</p>
<p>0&amp;0=0</p>
<p>0&amp;1=0</p>
<p>1&amp;0=0</p>
<p>1&amp;1=1</p>
<p>即两个操作数都为1时结果才为1，否则为0</p>
<h5 id="或运算符"><a href="#或运算符" class="headerlink" title="或运算符"></a>或运算符</h5><p>假设对两个二进制数做或运算如下:</p>
<p>0|0=0</p>
<p>0|1=1</p>
<p>1|0=1</p>
<p>1|1=1</p>
<p>即两个操作数只要有一个为1则结果为1。</p>
<h5 id="异或运算符"><a href="#异或运算符" class="headerlink" title="异或运算符"></a>异或运算符</h5><p>假设对两个二进制数做异或运算如下:</p>
<p>0^0=0</p>
<p>0^1=1</p>
<p>1^0=1</p>
<p>1^1=0</p>
<p>即两个操作数不相同时结果为1，否则为0。</p>
<h5 id="非运算符"><a href="#非运算符" class="headerlink" title="非运算符"></a>非运算符</h5><p>只有一个操作数，即取当前操作数的反码。参考<a href="https://TaffyBlog.github.io/">有符号数和无符号数</a></p>
<h5 id="左移和右移运算符"><a href="#左移和右移运算符" class="headerlink" title="左移和右移运算符"></a>左移和右移运算符</h5><p>右：</p>
<p>位右移运算将整个数按位右移若干位，右移后空出的部分补0。比如：8位的二进制数 01100101 将其右移3位，结果是00001100。</p>
<p>左：</p>
<p>位左移运算将整个数按位左移若干位，左移后空出的部分补0。比如：8位的二进制数01100101),将其左移3位，结果是00101000。</p>
<h3 id="加法运算"><a href="#加法运算" class="headerlink" title="加法运算"></a>加法运算</h3><h5 id="加法运算的原理"><a href="#加法运算的原理" class="headerlink" title="加法运算的原理"></a>加法运算的原理</h5><p>假设两个数num1、num2，求num1+num2，步骤如下：</p>
<ol>
<li>异或运算，num1^num2</li>
<li>用与运算判断是否有进位，num1&amp;num2。</li>
<li>如果第二步得到的结果为0，则num1+num2=num1^num2得到结果;如果第二步得到的结果不为0，将第二步得到的结果向左移一位(num1&amp;num2)&lt;&lt;1。</li>
<li>将第一步得到的结果与第三步得到的结果进行或异运算并判断是否有进位。</li>
<li>循环至第三步，直至没有进位为止。</li>
</ol>
<h5 id="代码示例"><a href="#代码示例" class="headerlink" title="代码示例"></a>代码示例</h5><pre class="line-numbers language-java"><code class="language-java"><span class="token keyword">int</span> <span class="token function">Add</span><span class="token punctuation">(</span><span class="token keyword">int</span> num1<span class="token punctuation">,</span> <span class="token keyword">int</span> num2<span class="token punctuation">)</span>
<span class="token punctuation">{</span>
    <span class="token keyword">int</span> sum <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>
    <span class="token keyword">while</span> <span class="token punctuation">(</span>num2 <span class="token operator">!=</span> <span class="token number">0</span><span class="token punctuation">)</span>
    <span class="token punctuation">{</span>
        <span class="token comment" spellcheck="true">//进行异或运算</span>
        sum <span class="token operator">=</span> num1 <span class="token operator">^</span> num2<span class="token punctuation">;</span>

        <span class="token comment" spellcheck="true">//使用与运算判断是否有进位，与运算的结果为0则没有进位。然后向左移一位。</span>
        num2 <span class="token operator">=</span> <span class="token punctuation">(</span>num1 <span class="token operator">&amp;</span> num2<span class="token punctuation">)</span> <span class="token operator">&lt;&lt;</span> <span class="token number">1</span><span class="token punctuation">;</span>

        <span class="token comment" spellcheck="true">//将异或运算结果给第一个操作数进行进位后的运算</span>
        num1 <span class="token operator">=</span> sum<span class="token punctuation">;</span>
    <span class="token punctuation">}</span><span class="token keyword">while</span> <span class="token punctuation">(</span>num2 <span class="token operator">!=</span> <span class="token number">0</span><span class="token punctuation">)</span><span class="token punctuation">;</span>

    <span class="token keyword">return</span> num1<span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h3 id="减法运算"><a href="#减法运算" class="headerlink" title="减法运算"></a>减法运算</h3><h5 id="减法运算的原理"><a href="#减法运算的原理" class="headerlink" title="减法运算的原理"></a>减法运算的原理</h5><p>减法和运算可以转化为加法，如:4-5=4+(-5);<br>减法就是将减数取补码，然后和被减数相加。</p>
<h5 id="代码示例-1"><a href="#代码示例-1" class="headerlink" title="代码示例"></a>代码示例</h5><pre class="line-numbers language-java"><code class="language-java"> <span class="token keyword">int</span> <span class="token function">Sub</span><span class="token punctuation">(</span><span class="token keyword">int</span> num1<span class="token punctuation">,</span><span class="token keyword">int</span> num2<span class="token punctuation">)</span>
<span class="token punctuation">{</span>

   <span class="token keyword">return</span> <span class="token function">Add</span><span class="token punctuation">(</span>num1<span class="token punctuation">,</span> <span class="token function">Complement</span><span class="token punctuation">(</span>num2<span class="token punctuation">)</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>

<span class="token keyword">int</span> <span class="token function">Complement</span><span class="token punctuation">(</span><span class="token keyword">int</span> num<span class="token punctuation">)</span> <span class="token comment" spellcheck="true">//取补码,,反码加1</span>
<span class="token punctuation">{</span>
    <span class="token keyword">return</span> <span class="token function">Add</span><span class="token punctuation">(</span><span class="token operator">~</span>num<span class="token punctuation">,</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>
<span class="token punctuation">}</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h3 id="乘法运算"><a href="#乘法运算" class="headerlink" title="乘法运算"></a>乘法运算</h3><h5 id="乘法运算的原理"><a href="#乘法运算的原理" class="headerlink" title="乘法运算的原理"></a>乘法运算的原理</h5><p>乘法就是将乘数写成(2^0)*k0 + (2^1)*k1 + (2 ^2)*k2 + … + (2^31)*k31，其中ki为0或1，然后利用位运算和加法就可以了。</p>
<pre class="line-numbers language-java"><code class="language-java"><span class="token comment" spellcheck="true">//正数乘法运算  </span>
<span class="token keyword">int</span> <span class="token function">Pos_Multiply</span><span class="token punctuation">(</span><span class="token keyword">int</span> a<span class="token punctuation">,</span><span class="token keyword">int</span> b<span class="token punctuation">)</span>  
<span class="token punctuation">{</span>  
    <span class="token keyword">int</span> ans <span class="token operator">=</span> <span class="token number">0</span><span class="token punctuation">;</span>  
    <span class="token keyword">while</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span>  
    <span class="token punctuation">{</span>  
        <span class="token keyword">if</span><span class="token punctuation">(</span>b<span class="token operator">&amp;</span><span class="token number">1</span><span class="token punctuation">)</span>  
            ans <span class="token operator">=</span> <span class="token function">Add</span><span class="token punctuation">(</span>ans<span class="token punctuation">,</span> a<span class="token punctuation">)</span><span class="token punctuation">;</span>  
        a <span class="token operator">=</span> <span class="token punctuation">(</span>a<span class="token operator">&lt;&lt;</span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>  
        b <span class="token operator">=</span> <span class="token punctuation">(</span>b<span class="token operator">>></span><span class="token number">1</span><span class="token punctuation">)</span><span class="token punctuation">;</span>  
    <span class="token punctuation">}</span>  
    <span class="token keyword">return</span> ans<span class="token punctuation">;</span>  
<span class="token punctuation">}</span>  

<span class="token comment" spellcheck="true">//乘法运算  </span>
<span class="token keyword">int</span> <span class="token function">Multiply</span><span class="token punctuation">(</span><span class="token keyword">int</span> a<span class="token punctuation">,</span><span class="token keyword">int</span> b<span class="token punctuation">)</span>  
<span class="token punctuation">{</span>  
    <span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token function">iszero</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span> <span class="token operator">||</span> <span class="token function">iszero</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span> <span class="token punctuation">)</span>  
        <span class="token keyword">return</span> <span class="token number">0</span><span class="token punctuation">;</span>  
    <span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token function">ispos</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span> <span class="token operator">&amp;&amp;</span> <span class="token function">ispos</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span> <span class="token punctuation">)</span>  
        <span class="token keyword">return</span> <span class="token function">Pos_Multiply</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span> b<span class="token punctuation">)</span><span class="token punctuation">;</span>  
    <span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token function">isneg</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span> <span class="token punctuation">)</span>  
    <span class="token punctuation">{</span>  
        <span class="token keyword">if</span><span class="token punctuation">(</span> <span class="token function">isneg</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span> <span class="token punctuation">)</span>  
        <span class="token punctuation">{</span>  
            <span class="token keyword">return</span> <span class="token function">Pos_Multiply</span><span class="token punctuation">(</span> <span class="token function">negtive</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">,</span> <span class="token function">negtive</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span> <span class="token punctuation">)</span><span class="token punctuation">;</span>  
        <span class="token punctuation">}</span>  
        <span class="token keyword">return</span> <span class="token function">negtive</span><span class="token punctuation">(</span> <span class="token function">Pos_Multiply</span><span class="token punctuation">(</span> <span class="token function">negtive</span><span class="token punctuation">(</span>a<span class="token punctuation">)</span><span class="token punctuation">,</span> b <span class="token punctuation">)</span> <span class="token punctuation">)</span><span class="token punctuation">;</span>  
    <span class="token punctuation">}</span>  
    <span class="token keyword">return</span> <span class="token function">negtive</span><span class="token punctuation">(</span> <span class="token function">Pos_Multiply</span><span class="token punctuation">(</span>a<span class="token punctuation">,</span> <span class="token function">negtive</span><span class="token punctuation">(</span>b<span class="token punctuation">)</span><span class="token punctuation">)</span> <span class="token punctuation">)</span><span class="token punctuation">;</span>  
<span class="token punctuation">}</span>  
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<h3 id="除法运算"><a href="#除法运算" class="headerlink" title="除法运算"></a>除法运算</h3><h5 id="原理"><a href="#原理" class="headerlink" title="原理"></a>原理</h5><p>除法就是由乘法的过程逆推，依次减掉（如果x够减）y^(2^31),y^(2^30),…y^8,y^4,y^2,y^1。减掉相应数量的y就在结果加上相应的数量。</p>
<pre class="line-numbers language-java"><code class="language-java"><span class="token keyword">int</span> <span class="token function">Pos_Div</span><span class="token punctuation">(</span><span class="token keyword">int</span> x<span class="token punctuation">,</span><span class="token keyword">int</span> y<span class="token punctuation">)</span>  
<span class="token punctuation">{</span>  
    <span class="token keyword">int</span> ans<span class="token operator">=</span><span class="token number">0</span><span class="token punctuation">;</span>  
    <span class="token keyword">for</span><span class="token punctuation">(</span><span class="token keyword">int</span> i<span class="token operator">=</span><span class="token number">31</span><span class="token punctuation">;</span>i<span class="token operator">>=</span><span class="token number">0</span><span class="token punctuation">;</span>i<span class="token operator">--</span><span class="token punctuation">)</span>  
    <span class="token punctuation">{</span>  
        <span class="token comment" spellcheck="true">//比较x是否大于y的(1&lt;&lt;i)次方，避免将x与(y&lt;&lt;i)比较，因为不确定y的(1&lt;&lt;i)次方是否溢出  </span>
        <span class="token keyword">if</span><span class="token punctuation">(</span><span class="token punctuation">(</span>x<span class="token operator">>></span>i<span class="token punctuation">)</span><span class="token operator">>=</span>y<span class="token punctuation">)</span>  
        <span class="token punctuation">{</span>  
            ans<span class="token operator">+=</span><span class="token punctuation">(</span><span class="token number">1</span><span class="token operator">&lt;&lt;</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>  
            x<span class="token operator">-=</span><span class="token punctuation">(</span>y<span class="token operator">&lt;&lt;</span>i<span class="token punctuation">)</span><span class="token punctuation">;</span>  
        <span class="token punctuation">}</span>  
    <span class="token punctuation">}</span>  
    <span class="token keyword">return</span> ans<span class="token punctuation">;</span>  
<span class="token punctuation">}</span>
<span aria-hidden="true" class="line-numbers-rows"><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span><span></span></span></code></pre>
<p><a href="http://blog.csdn.net/hackbuteer1/article/details/7390093" target="_blank" rel="noopener">代码参考文章</a></p>

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